[31] The diagonal always giving the resultant when each side represents a force; and if we look on the resultant as a compound force, a comparison of diagonals becomes a comparison of compounds.
[32] A law of nature being merely a generalization of relations, and having no existence except in the mind, is essentially intangible; and therefore, however small the law may be, it can never admit of exceptions, though its operation may admit of innumerable exceptions. Hence, as Dugald Stewart (Philosophy of the Mind, vol. ii. p. 211) rightly says, we can only refer to the laws of nature ‘by a sort of figure or metaphor.’ This is constantly lost sight of even by authors of repute; some of whom speak of laws as if they were causes, and therefore liable to interruption by larger causes; while other writers pronounce them to be ‘delegated agencies’ from the Deity. Compare Prout's Bridgewater Treatise, pp. 318, 435, 495; Sadler's Law of Population, vol. ii. p. 67; Burdach's Physiologie, vol. i. p. 160. Mr. Paget, in his able work, Lectures on Pathology, vol. i. p. 481, vol. ii. p. 542, with much greater accuracy calls such cases ‘apparent exceptions’ to laws; but it would be better to say, ‘exceptions to the operations of laws.’ The context clearly proves that Mr. Paget distinctly apprehends the difference; but a slight alteration of this kind would prevent confusion in the minds of ordinary readers.
[33] Mr. Rawson, in his Inquiry into the Statistics of Crime in England and Wales (published in the Journal of the Statistical Society, vol. ii. pp. 316–344), says, p. 327, ‘No greater proof can be given of the possibility of arriving at certain constants with regard to crime, than the fact which appears in the following table, that the greatest variation which has taken place during the last three years, in the proportion of any class of criminals at the same period of life, has not exceeded a half per cent.’ See also Report of British Association for 1839, Transac. of Sec., p. 118. Indeed, all writers who have examined the evidence are forced to admit this regularity, however they may wish to explain it. M. Dufau (Traité de Statistique, p. 144) says, ‘Les faits de l'ordre moral sont, aussi bien que ceux de l'ordre naturel, le produit de causes constantes et régulières,’ &c.; and at p. 367, ‘C'est ainsi que le monde moral se présente à nous, de ce point de vue, comme offrant, de même que le monde physique, un ensemble continu d'effets dus à des causes constantes et régulières, dont il appartient surtout à la statistique de constater l'action.’ See to the same effect Moreau-Christophe des Prisons en France, Paris, 1838, pp. 53, 189.
[34] ‘It is curious to observe how intimate a relation exists between the price of food and the number of marriages.’ … ‘The relation that subsists between the price of food and the number of marriages is not confined to our own country; and it is not improbable that, had we the means of ascertaining the facts, we should see the like result in every civilized community. We possess the necessary returns from France; and these fully bear out the view that has been given.’ Porter's Progress of the Nation, vol. ii. pp. 244, 245, London, 1838.
[35] ‘The marriage returns of 1850 and 1851 exhibit the excess which since 1750 has been invariably observed when the substantial earnings of the people are above the average.’ Journal of Statistical Society, vol. xv. p. 185.
[36] See Somerville's Physical Geography, vol. ii. pp. 409–411, which, says this able writer, proves that ‘forgetfulness as well as free will is under constant laws.’ But this is using the word ‘free will’ in a sense different from that commonly employed.
[37] Achenwall, in the middle of the eighteenth century, is usually considered to be the first systematic writer on statistics, and is said to have given them their present name. See Lewis, Methods of Observation and Reasoning in Politics, 1852, vol. i. p. 72; Biographie Universelle, vol. i. p. 140; Dufau, Traité de Statistique, pp. 9, 10. Even so late as 1800, the Bishop of Llandaff wrote to Sir John Sinclair, ‘I must think the kingdom is highly indebted to you for bringing forward a species of knowledge (statistics) wholly new in this country, though not new in other parts of Europe.’ Sinclair's Correspondence, vol. i. p. 230. Sinclair, notwithstanding his industry, was a man of slender powers, and did not at all understand the real importance of statistics, of which, indeed, he took a mere practical view. Since then statistics have been applied extensively to medicine; and still more recently, and on a smaller scale, to philology and to jurisprudence. Compare Bouillaud, Philosophie Médicale, pp. 96, 186; Renouard, Hist. de la Médecine, vol. ii. pp. 474, 475; Esquirol, Maladies Mentales, vol. ii. pp. 665–667; Holland's Medical Notes, pp. 5, 472; Vogel's Pathological Anatomy, pp. 15–17; Simon's Pathology, p. 180; Phillips on Scrofula, pp. 70, 118, &c.; Prichard's Physical Hist. of Mankind, vol. iv. p. 414; Eschbach, Etude du Droit, pp. 392–394.
CHAPTER II.
INFLUENCE EXERCISED BY PHYSICAL LAWS OVER THE ORGANIZATION OF SOCIETY AND OVER THE CHARACTER OF INDIVIDUALS.